Problem: Solve for $x$ and $y$ using substitution. ${-x+2y = 6}$ ${y = -3x-11}$
Solution: Since $y$ has already been solved for, substitute $-3x-11$ for $y$ in the first equation. ${-x + 2}{(-3x-11)}{= 6}$ Simplify and solve for $x$ $-x-6x - 22 = 6$ $-7x-22 = 6$ $-7x-22{+22} = 6{+22}$ $-7x = 28$ $\dfrac{-7x}{{-7}} = \dfrac{28}{{-7}}$ ${x = -4}$ Now that you know ${x = -4}$ , plug it back into $\thinspace {y = -3x-11}\thinspace$ to find $y$ ${y = -3}{(-4)}{ - 11}$ $y = 12 - 11$ $y = 1$ You can also plug ${x = -4}$ into $\thinspace {-x+2y = 6}\thinspace$ and get the same answer for $y$ : ${-}{(-4)}{ + 2y = 6}$ ${y = 1}$